GeoFusion-CAD: Structure-Aware Diffusion with Geometric State Space for Parametric 3D Design

Xiaolei Zhou; Chuangjie Fang; Jie Wu; Jingyi Yang; Boyi Lin; Jianwei Zheng

cs.CVMar 23, 2026

GeoFusion-CAD: Structure-Aware Diffusion with Geometric State Space for Parametric 3D Design

Authors: Xiaolei Zhou, Chuangjie Fang, Jie Wu, Jingyi Yang, Boyi Lin, Jianwei Zheng

Organizations: Zhejiang University of Technology · Hangzhou International Innovation Institute, Beihang University

Abstract

Parametric Computer-Aided Design (CAD) is fundamental to modern 3D modeling, yet existing methods struggle to generate long command sequences, especially under complex geometric and topological dependencies. Transformer-based architectures dominate CAD sequence generation due to their strong dependency modeling, but their quadratic attention cost and limited context windowing hinder scalability to long programs. We propose GeoFusion-CAD, an end-to-end diffusion framework for scalable and structure-aware generation. Our proposal encodes CAD programs as hierarchical trees, jointly capturing geometry and topology within a state-space diffusion process. Specifically, a lightweight C-Mamba block models long-range structural dependencies through selective state transitions, enabling coherent generation across extended command sequences. To support long-sequence evaluation, we introduce DeepCAD-240, an extended benchmark that increases the sequence length ranging from 40 to 240 while preserving sketch-extrusion semantics from the ABC dataset. Extensive experiments demonstrate that GeoFusion-CAD achieves superior performance on both short and long command ranges, maintaining high geometric fidelity and topological consistency where Transformer-based models degrade. Our approach sets new state-of-the-art scores for long-sequence parametric CAD generation, establishing a scalable foundation for next-generation CAD modeling systems. Code and datasets are available at GitHub.

Figures & tables

Figure 1: CAD construction pipeline and hierarchical representation. Sequential Sketch and Extrusion operations form a 3D solid, which is encoded by GeoFusion-CAD into a hierarchical tree capturing geometry and topology.

Figure 2: Comparison between transformer-based CAD architecture and ours. (Left) The transformer-based method trains command and argument sequences separately. (Right) Our GeoFusion-CAD models the hierarchical CAD topology with G-Mamba blocks, mapping solid and hierarchical topology into a unified sequence.

Figure 3: Overview of GeoFusion-CAD. The framework consists of two embedding layers, a G-Mamba diffusion encoder, and a CAD decoder. Each parent node conditions its child node during the reverse diffusion process, enabling structured and coherent generation.

Figure 4: Architecture of G-Mamba Blocks. The block consists of a DWC module, a GSM-SSD layer, and an MLP, enabling geometry-conditioned multi-scale state transitions.

Figure 5: Visual results on different test ranges. Compared with others, GeoFusion-CAD produces coherent solids with fewer surface artifacts. Some subtle abnormities are marked in red circles.

Test Range	Model	ACC ${}_{cmd}\uparrow$	ACC ${}_{param}\uparrow$	ACC ${}_{line}\uparrow$	ACC ${}_{arc}\uparrow$	ACC ${}_{Circle}\uparrow$	ACC ${}_{ext}\uparrow$	COV $\uparrow$	MMD $\downarrow$	JSD $\downarrow$	Memory	FLOPs(256)
DeepCAD	DeepCAD	92.4	89.2	85.4	87.3	87.2	90.1	78.1	1.72	3.98	–	–
	SkexGen	94.6	91.3	89.1	91.1	91.7	92.2	81.2	1.49	3.58	–	–
	HNC-CAD	95.4	93.8	88.3	94.5	94.7	94.7	82.3	1.33	3.24	–	–
	Ours	99.3	97.6	93.5	97.2	96.3	98.6	85.6	0.95	2.51	–	–
DeepCAD-240	DeepCAD	75.2	72.5	76.1	77.6	79.3	77.3	64.5	1.85	4.09	8197MiB	52.8G
	SkexGen	81.4	78.3	78.1	81.8	81.6	81.7	68.9	1.78	3.97	11235MiB	91.2G

Table 1: Quantitative comparison and complexity analysis (×

10^{2}

) under DeepCAD and DeepCAD-240 test sets.

\uparrow

indicates higher is better,

\downarrow

lower is better. All models are trained on the unified DeepCAD-240 dataset.

Model	ACC ${}_{cmd}\uparrow$	ACC ${}_{param}\uparrow$	COV $\uparrow$	MMD $\downarrow$	JSD $\downarrow$
w/o Tree	87.5	84.6	69.4	1.46	3.25
MLP	75.3	72.1	67.8	1.73	3.81
Transformer	82.6	81.3	69.1	1.55	3.67
Vanilla Mamba	89.2	87.6	72.7	1.19	3.05
Ours	91.2	89.3	73.9	1.12	2.97

Table 2: Ablation study on the DeepCAD-240 test set.

\uparrow

indicates higher is better,

\downarrow

lower is better. “w/o Tree” denotes the model trained without hierarchical encoding.

Sequence Type	Token Type	Token Value	Token Representation	Description
Structure & Control	pad	0	$(0,0)$	Padding Token
	cls	1	$(1,0)$	Start Token
	end	1	$(1,0)$	End Token
	$e_{solid}$	2	$(2,0)$	End Solid
	$e_{sketch}$	3	$(3,0)$	End Sketch
	$e_{face}$	4	$(4,0)$	End Face

Table S1 : CAD sequence representation (Explicit Hierarchy without Revolution). Continuous parameters are uniformly quantized into

[11,266]

. Note the inclusion of Face-level hierarchy (

e_{f}

) and explicit primitive parameters.

Figure S1 : Illustration of the sketch–extrusion sequence construction. Each CAD model is decomposed into a procedural chain of sketches and extrusions. The process begins with 2D sketch definition and proceeds through sequential extrusion operations, progressively forming a coherent solid structure. This sequence explicitly encodes design history, preserving both geometric and topological dependencies across modeling stages.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Total	Avg. Length	1–40	40–60	60–80	80–160	160–240
DeepCAD [ 32 ]	178,238	15	44.58	55.42	–	–	–
DeepCAD-240 (Ours)	215,914	36.2	76.6	12.0	5.9	5.2	0.21

Appendix

Table S2 : Statistical comparison between the original DeepCAD dataset and our extended DeepCAD-240 dataset, including total samples, average command length, and sequence length distribution (%).

Figure S2 : Distribution of CAD command sequences lengths in the DeepCAD-240.

Figure S3 : Additional qualitative comparisons. Each row shows representative CAD samples generated by DeepCAD, HNC-CAD, and our GeoFusion-CAD, along with ground-truth models. GeoFusion-CAD consistently produces geometrically complete and watertight solids with smooth curvature and accurate local features, while baseline methods often exhibit surface distortions, missing connections, or inconsistent boolean joins in complex structures. These examples further demonstrate that the combination of hierarchical tree encoding and G-Mamba diffusion yields improved geometric stability and scalability across extended command sequences.

Model	ACC ${}_{cmd}\uparrow$	ACC ${}_{param}\uparrow$	ACC ${}_{line}\uparrow$	ACC ${}_{arc}\uparrow$	ACC ${}_{circle}\uparrow$	ACC ${}_{ext}\uparrow$	COV $\uparrow$	MMD $\downarrow$	JSD $\downarrow$
Flat Sequence (w/o Tree)	87.5	84.6	79.3	71.5	73.2	81.1	69.4	1.46	3.25
With Tree (Ours)	91.2	89.3	84.2	89.8	86.8	94.9	73.9	1.12	2.97

Appendix

Table S3 : Ablation on hierarchical tree representation on the DeepCAD-240 test set.

\uparrow

indicates higher is better,

\downarrow

lower is better.

Model	ACC ${}_{cmd}\uparrow$	ACC ${}_{param}\uparrow$	ACC ${}_{line}\uparrow$	ACC ${}_{arc}\uparrow$	ACC ${}_{circle}\uparrow$	ACC ${}_{ext}\uparrow$	COV $\uparrow$	MMD $\downarrow$	JSD $\downarrow$
MLP (replace G-Mamba)	75.3	72.1	66.8	60.5	63.7	68.2	67.8	1.73	3.81
U-Net (replace G-Mamba)	80.4	78.6	71.2	64.3	67.8	72.1	70.2	1.37	3.45
Transformer (replace G-Mamba)	82.6	81.3	74.9	67.6	69.8	76.3	69.1	1.55	3.67
Vanilla Mamba (replace G-Mamba)	89.2	87.6	82.1	78.5	82.4	89.1	72.7	1.19	3.05
Full (G-Mamba, Ours)	91.2	89.3	84.2	89.8	86.8	94.9	73.9	1.12	2.97

Appendix

Table S4 : Ablation on the G-Mamba diffusion block compared with standard alternatives.

\uparrow

indicates higher is better,

\downarrow

lower is better.

Figure S4 : Additional CAD modeling results generated by GeoFusion-CAD. The results cover a variety of industrial-style parts, including prismatic, rotational, and mixed-form geometries. The generated solids are watertight, structurally coherent, and geometrically precise, demonstrating the robustness and generalization of our approach.

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Parametric CAD Modeling Diffusion Models

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Recent deep learning approaches seek to automate CAD creation by representing a model as a sequence of discrete commands and parameters, and then generating them using autoregressive models or continuous diffusion operating in Euclidean embedding space. However, continuous diffusion perturbs representations in a continuous Euclidean domain that does not reflect the inherently discrete and heterogeneous nature of CAD tokens, often producing perturbed representations that map to semantically invalid symbols. To overcome this limitation, we propose a cascaded discrete diffusion framework for CAD generation, which consists of a command diffusion for generating CAD commands and a parameter diffusion conditioned on CAD commands. Unlike isotropic Gaussian perturbation, the forward process of our approach operates directly over categorical token distributions using delicate transition matrices. For commands, we adopt an absorbing-state transition matrix that progressively corrupts tokens to a designated symbol; for parameters, we introduce specific transition matrices tailored to heterogeneous attributes: a Gaussian kernel for coordinate continuity, a scale-invariant kernel for dimensional values, and a prior-preserving kernel for boolean attributes. The reverse process is achieved by two denoising networks: a Transformer-based encoder for command recovery, and a parameter network with extra local self-attention for command-level interaction and cross-attention for conditional injection. Experiments on the DeepCAD dataset show that the proposed approach surpasses existing autoregressive and continuous diffusion models on unconditional generation metrics, while qualitative results validate effective controllability in conditional generation tasks. Source codes will be released.

Abstract

Parametric CAD Modeling

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